Another useful property of the relaxation time is that contracting vertices of a weighted graph can never increase it. That is, whenever a set \(A\)  of vertices of a graph \(G\)  are replaced by a single vertex \(a\) , and each edge \((u,v)\)  is replaced by an edge \((u,a)\)  of the same weight as \((u,v)\)  whenever \(v \in A\)  (consequently every edge within \(A\)  becomes a loop at \(a\)  of that weight), the new graph \(G_A\)  thus formed has (Corollary 3.27 of [1]})
\(\tau _2(G_A) \le \tau _2(G).\) 
